Convection in a very compressible fluid: comparison of simulations with experiments

Perturbation-controlled numerical simulations of the convection onset in a supercritical fluid layer

This paper reports 2D and 3D direct numerical simulations of the Rayleigh-Bénard convection in a fluid layer, 3He, close to its gas-liquid critical point. The main quantity of interest is the time when the convective motion becomes appreciable after the heat current has been started. A space periodic, time-independent temperature perturbation is applied to the top plate aiming to represent the various sources of noise in the experiments. A single amplitude of this additional perturbation reproduces the noise level of the experiments for all the used combinations of the critical point proximity and of the heating power. Over four decades of the Rayleigh number, this simple operation removes the systematic discrepancy reported in an earlier paper and brings the simulations into good agreement with the measurements. Scaling of the exponential convection growth rate is presented and discussed.

Onset of the convection in a supercritical fluid

A model is proposed that leads to the scaled relation tp/tau D=Ftp(Ra-Rac) for the development of convection in a pure fluid in a Rayleigh-Bénard cell after the start of the heat current at t=0. Here tp is the time of the first maximum of the temperature drop DeltaT(t) across the fluid layer, the signature of rapidly growing convection, tau D is the diffusion relaxation time, and Rac is the critical Rayleigh number. Such a relation was first obtained empirically from experimental data. Because of the unknown perturbations in the cell that lead to convection development beyond the point of the fluid instability, the model determines tp/tau D within a multiplicative factor Psi square root Rac(HBL), the only fit parameter product. Here Rac(HBL), of the order 10(3), is the critical Rayleigh number of the hot boundary layer and Psi is a fit parameter. There is then good agreement over more than four decades of Ra-Rac between the model and the experiments on supercritical 3He at various heat currents and temperatures. The value of the parameter Psi, which phenomenologically represents the effectiveness of the perturbations, is discussed in connection with predictions by El Khouri and Carlès of the fluid instability onset time.

Numerical simulation studies of the convective instability onset in a supercritical fluid

Numerical simulation studies in 2D with the addition of noise are reported for the convection of a supercritical fluid, 3He , in a Rayleigh-Bénard cell. The noise addition is to accelerate the instability growth after starting the heat flow across the fluid, so as to bring simulations into better agreement with published experimental observations. Homogeneous temperature noise and spatial longitudinal periodic temperature variations in either top or bottom plates were programmed into the simulations. The second method was the most effective in speeding up the instability onset. For a small amplitude of the longitudinal perturbations, a semiquantitative agreement with the observations was obtained. The results are discussed in relation to predictions by El Khouri and Carlès.

Scaling behavior for the onset of convection in a colloidal suspension

We investigate the early stages of mass convection in a colloidal suspension at high solutal Rayleigh number Ras. From the time evolution of shadowgraph images and by assuming a diffusive growth of the boundary layers we obtain an indirect measurement of the concentration boundary layer thickness delta* at the onset of convection. We show that the dimensionless boundary layer thickness delta=delta*/d scales as Ra-ps, where Ras=Rasdelta is a modified solutal Rayleigh number for convection which accounts for the actual density unbalance and d is the thickness of the sample layer. This scaling behavior is analogous to that reported at steady state for turbulent convection in simple fluids. We find p=0.35, a value compatible with the exponent 1/3, reported for turbulent heat convection in simple fluids at steady state.